Place apricots, lemon juice, white sugar in a small saucepan. Add enough water to just cover the apricots. Bring to a boil, and cook until fruit is soft. Chop coarsely.
Sift flour, oatmeal and brown sugar together. Melt butter or margarine over low heat and stir into flour mixture. Put 2/3 of this mixture into 8 x 8 inch greased pan. Spread apricot mixture over crust. Sprinkle remaining oatmeal mixture over apricots.